How do I cycle through the camera views?
You can try by binding the cameras to the markers. In the timeline, press M to add marker in specified frames. You can rename that frame by pressing Ctrl + M.

Assuming you have 2 cameras on viewport, then add two marker on timeline (adjust location of the marker diferently, ie : marker 1 : 1-20, marker 2 : 21-50). Now select the first camera, press Ctrl + 0 to set as active camera, make sure first marker selected, then in timeline press Ctrl + B to bind active camera to first marker.

Select the second marker, then set second camera as active again Ctrl + 0, hover the mouse on the timeline and press Ctrl + B.

Now, when you start the animation Alt + A, the camera should switch between first and second based on marker position.